To find the kinetic energy (KE) of the bowling ball, we can use the formula:
\[ KE = \frac{1}{2}mv^2 \]
Where:
- \(m\) is the mass of the object in kilograms (6 kg for the bowling ball),
- \(v\) is the velocity in meters per second (7.6 m/s).
Plugging in the values:
\[ KE = \frac{1}{2} \times 6 , \text{kg} \times (7.6 , \text{m/s})^2 \]
First, we calculate \( (7.6 , \text{m/s})^2 \):
\[ (7.6)^2 = 57.76 , \text{m}^2/\text{s}^2 \]
Now substitute back into the equation:
\[ KE = \frac{1}{2} \times 6 \times 57.76 \]
Calculating further:
\[ KE = 3 \times 57.76 = 173.28 , \text{J} \]
So, the kinetic energy of the bowling ball when it hits the pin is 173.28 J.